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lfunc_lfunctions • Show schema
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{'Lhash': '2359414708751059205897144435555', 'a10': [-3.1669285009917974e-05, -0.00013054257081145907], 'a2': [0.32706796331742166, 0.9450008187146685], 'a3': [0.4582265217274104, -0.8888354486549235], 'a4': [-0.7860530947427875, 0.6181589862206052], 'a5': [-0.00013372084484185922, -1.2768792499043547e-05], 'a6': [0.9898214418809327, 0.14231483827328514], 'a7': [1.2602361304963487, -2.3263286301362474], 'a8': [-0.8412535328311812, -0.5406408174555976], 'a9': [-0.5800569095711982, -0.8145759520503357], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.713548835255689, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.32706796331742166, -0.9450008187146685]]], [3, [[1.0, 0], [-0.4582265217274104, 0.8888354486549235]]], [7, [[1.0, 0], [-1.2602361304963487, 2.3263286301362474]]], [23, [[1.0, 0], [-3.5926496325095427, 3.1769275437172073]]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '966.145', 'coefficient_field': 'CDF', 'conductor': 966, 'conductor_radical': 966, 'conjugate': '772768149346038226814884324227', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.32706796331742166, -0.9450008187146685]], [[1.0, 0], [-0.4582265217274104, 0.8888354486549235]], [[1.0, 0], [0.00013372084484185922, 1.2768792499043547e-05], [4.909643486313533, 0.946256221802051]], [[1.0, 0], [-1.2602361304963487, 2.3263286301362474]], [[1.0, 0], [2.187892586995996, 0.7572369866931604], [8.646584042170662, 6.799748848426657]], [[1.0, 0], [-1.485905536467823, 5.06052952374335], [-10.936295926805355, -7.028330626922768]], [[1.0, 0], [4.725913166631315, -1.8919702310713704], [12.303478647786193, -11.731343195195905]], [[1.0, 0], [2.450882282550222, 0.9811852556213118], [13.750946723996334, 13.111501218160127]], [[1.0, 0], [-3.5926496325095427, 3.1769275437172073]], [[1.0, 0], [0.04780481369394513, -0.332489782467557], [-27.825296234820424, -8.170244148401462]], [[1.0, 0], [-0.4790475691671265, 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70.94224448761854]], [[1.0, 0], [-1.82033617804673, -1.9091136390556056], [-3.7589713500756416, 78.91051979545763]], [[1.0, 0], [2.171208602960037, -4.754283673018014], [-54.35344091745866, -62.72721467140344]], [[1.0, 0], [0.3541723096492189, 7.434991770026459], [-88.59700110900452, 8.459987854072256]], [[1.0, 0], [7.723584146142807, 16.9122902116022], [-63.52149119269265, 73.30770871236305]], [[1.0, 0], [-0.7027596932565912, -7.3596324719127795], [-99.17479842353337, 19.11437568040143]], [[1.0, 0], [-0.547116520833002, 0.10544806630708135], [95.62189710065547, -38.28123293301373]], [[1.0, 0], [-4.081405890344487, -7.9168229329275555], [-62.0660893241182, 87.15962686938592]], [[1.0, 0], [2.9449496160349544, 7.3561285145614], [-78.88701015345265, 75.21861225155021]], [[1.0, 0], [-10.420897377165687, -9.029758978839133], [16.08157672488122, 111.8498229325454]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 28, 'label': '2-966-161.145-c1-0-28', 'load_key': 'CMFs-workshop', 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'10.20005614045243921523853866821056'], 'prelabel': '2-966-161.145-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.777327642763037, 'root_angle': 0.19247438946228063, 'root_number': '0.3536253668840233 + 0.9353871390478596*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.192474389462', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.86125002293713048936866202005', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.65248536768127760166462667133', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.98215523124711468455405989963', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.713548835255689, 'bad_primes': [2, 3, 7, 23], 'central_character': '161.145', 'conductor': 966, 'conductor_radical': 966, 'degree': 2, 'index': 28, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/966/2/be/a/145/13'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-966-161.145-c1-0-28', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-966-161.145-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.777327642763037, 'root_angle': 0.19247438946228063, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.86125002293713048936866202005', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2359414708751059205897144435555', 'Lhash_array': ['2359414708751059205897144435555'], 'factors': ['2-966-161.145-c1-0-28'], 'label': '2-966-161.145-c1-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/966/2/be/a/145/13'}